High-quality, high-strength periodic magnetic fields are required in free electron lasers and as insertion devices for synchrotron radiation generation. The devices that provide the desired magnetic fields are referred to as undulators (or wigglers). They have taken several forms in the past, but all forms are characterized by the period of the magnetic field along an axis and by the transverse size of the magnetic field.
Originally, undulators were implemented as linear arrays of electromagnets with spatially-alternating excitation to generate the desired magnetic fields. However, such implementations were bulky and difficult to maintain.
It has long been known that rare-earth permanent magnets (REPMs) are useful in forming the desired periodic magnetic fields. Two parallel linear arrays of separate magnetized permanent magnets arranged along an axis and separated by a gap can produce the desired periodic magnetic field when the fields of the magnets are arranged in the proper sequence. The distribution of the magnetic fields is determined by the strength and magnetic orientation of the REPMs in the arrays.
In a later development, reported in Journal de Physique (Paris), vol. 44, p. C1-211 (1983), K. Halbach proposed a REPM-steel hybrid undulator that produces higher magnetic field strengths and higher field quality than are possible with a pure-REPM undulator. The REPM-steel undulator uses steel pole pieces interposed between the permanent magnets to improve the magnetic field distribution along the axis. The relative permeability of these steel pole pieces is much greater than one. The presence of the highly permeable pole pieces in the hybrid undulator drastically reduces the sensitivity of the design to magnetic orientation errors of the individual permanent magnets. The hybrid undulator's field distribution is determined primarily by pole shape and position, rather than the material properties. Therefore, the REPM material that can be used by the hybrid design can be less expensive and less well characterized than the material used in the pure-REPM undulator. However, a larger volume of REPM material is generally required.
The pole pieces cause the magnet surfaces that face the gap to be driven at a higher magnetic force, thereby increasing the on-axis magnetic field strength. Unfortunately, this conventional hybrid undulator suffers from magnetic field saturation of the poles. This, in turn, affects the field uniformity within the gap. In addition, the periodic magnetic fields they produced had undesirable high order frequency components.
It is, therefore, desirable to have an REPM hybrid undulator that can produce higher on-axis magnetic field strength and greater field uniformity in the gap, while avoiding pole saturation.